Everything Maths Grade 12

2.12 CHAPTER 2. LOGARITHMS

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(1.) 01br (2.) 01bs

Example 7: Logs in Compound Interest

QUESTION

I have R12 000 to invest. I need the money to grow to at leastR30 000. If it is invested at a

compound interest rateof 13% per annum, for how long (in full years) does my investment

need to grow?

SOLUTION

Step 1 : The formula to use

A = P (1 +i)n

Step 2 : Substitute and solve for n

30000 < 12000(1 + 0,13)n

1 , 13 n >

5

2

n log(1,13) > log(2,5)

n > log(2,5)÷ log(1,13)

n > 7 , 4972 ...

Step 3 : Determine the final answer

In this case we roundup, because 7 years will not yet deliver the required

R30 000. The investment need tostay in the bank for at least 8 years.

Chapter 2 End of Chapter Exercises

1. Show that
   loga

�

x

y

�

= loga(x)− loga(y)